scholarly journals Continuous-Time Multiobjective Optimization Problems via Invexity

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Valeriano A. De Oliveira ◽  
Marko A. Rojas-Medar
Keyword(s):  
Continuous Time ◽  
Efficient Solution ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Weakly Efficient Solution ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Relationship Of ◽  
The Relationship ◽  
Multiobjective Programming Problems

We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution to be a weakly efficient solution.

Multiobjective Programming

2014 ◽  
pp. 1585-1604
Author(s):  
Minghe Sun
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Objective Functions ◽  
Solution Quality ◽  
Solution Methods ◽  
Multiobjective Programming Problem ◽  
Feasible Solutions ◽  
Multiobjective Programming Problems

Optimization problems with multiple criteria measuring solution quality can be modeled as multiobjective programming problems. Because the objective functions are usually in conflict, there is not a single feasible solution that can optimize all objective functions simultaneously. An optimal solution is one that is most preferred by the decision maker (DM) among all feasible solutions. An optimal solution must be nondominated but a multiobjective programming problem may have, possibly infinitely, many nondominated solutions. Therefore, tradeoffs must be made in searching for an optimal solution. Hence, the DM's preference information is elicited and used when a multiobjective programming problem is solved. The model, concepts and definitions of multiobjective programming are presented and solution methods are briefly discussed. Examples are used to demonstrate the concepts and solution methods. Graphics are used in these examples to facilitate understanding.

scholarly journals Performances Assessment of MOMA-Plus Method on Multiobjective Optimization Problems

2020 ◽  
Vol 13 (1) ◽  
pp. 48-68
Author(s):  
Alexandre Som ◽  
Kounhinir Some ◽  
Abdoulaye Compaore ◽  
Blaise Some
Keyword(s):  
Multiobjective Optimization ◽  
Comparative Study ◽  
Pareto Front ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Non Linear

This work is devoted to evaluate the performances of the MOMA-plus method in solving multiobjective optimization problems. This assessment is doing on the complexity of its algorithm, the convergence and the diversity of solutions in relation to the Pareto front. All these parameters were evaluated on non-linear multiobjective test problems and obtained solutions are compared with those provided by the NSGA-II method. This comparative study made it possible tohighlight the performances of MOMA-plus method for solving non-linear multiobjective problems.

scholarly journals Variational-like inequalities for n-dimensional fuzzy-vector-valued functions and fuzzy optimization

2019 ◽  
Vol 17 (1) ◽  
pp. 627-645
Author(s):  
Ting Xie ◽  
Zengtai Gong
Keyword(s):  
Variational Inequality ◽  
Fuzzy Number ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Decomposition Theorem ◽  
Variational Inequality Problems ◽  
Multiobjective Optimization Problems ◽  
Vector Valued Functions ◽  
The Relationship ◽  
Vector Valued

Abstract The existing results on the variational inequality problems for fuzzy mappings and their applications were based on Zadeh’s decomposition theorem and were formally characterized by the precise sets which are the fuzzy mappings’ cut sets directly. That is, the existence of the fuzzy variational inequality problems in essence has not been solved. In this paper, the fuzzy variational-like inequality problems is incorporated into the framework of n-dimensional fuzzy number space by means of the new ordering of two n-dimensional fuzzy-number-valued functions we proposed [Fuzzy Sets and Systems 295 (2016) 19-36]. As a theoretical basis, the existence and the basic properties of the fuzzy variational inequality problems are discussed. Furthermore, the relationship between the variational-like inequality problems and the fuzzy optimization problems is discussed. Finally, we investigate the optimality conditions for the fuzzy multiobjective optimization problems.

scholarly journals A Simple Approach for Finding a Fair Solution to Multiobjective Programming Problems

2012 ◽  
Vol 2 ◽  
pp. 21-25 ◽  
Author(s):  
P. Pandian
Keyword(s):  
Efficient Solution ◽  
Multiobjective Programming ◽  
Simple Approach ◽  
Decision Makers ◽  
Multiple Objective ◽  
New Approach ◽  
Multi Objective Programming ◽  
Multiple Objective Decision Making ◽  
Multiobjective Programming Problems ◽  
Better Than

A new approach, namely sum of objectives (SO) method is proposed to finding a fair solution to multi-objective programming problems. The proposed method is very simple, easy to use and understand and also, common approaches. It is illustrated with the help of numerical examples. The fair solution serves more better than efficient solution for decision makers when they are handling multiple objective decision making problems.

scholarly journals Approximation Methods for Multiobjective Optimization Problems: A Survey

2021 ◽  
Author(s):  
Arne Herzel ◽  
Stefan Ruzika ◽  
Clemens Thielen
Keyword(s):  
Approximation Algorithms ◽  
Multiobjective Optimization ◽  
Operations Research ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Wide Range

Algorithms for approximating the nondominated set of multiobjective optimization problems are reviewed. The approaches are categorized into general methods that are applicable under mild assumptions and, thus, to a wide range of problems, and into algorithms that are specifically tailored to structured problems. All in all, this survey covers 52 articles published within the last 41 years, that is, between 1979 and 2020. Summary of Contribution: In many problems in operations research, several conflicting objective functions have to be optimized simultaneously, and one is interested in finding Pareto optimal solutions. Because of the high complexity of finding Pareto optimal solutions and their usually very large number, however, the exact solution of such multiobjective problems is often very difficult, which motivates the study of approximation algorithms for multiobjective optimization problems. This research area uses techniques and methods from algorithmics and computing in order to efficiently determine approximate solutions to many well-known multiobjective problems from operations research. Even though approximation algorithms for multiobjective optimization problems have been investigated for more than 40 years and more than 50 research articles have been published on this topic, this paper provides the first survey of this important area at the intersection of computing and operations research.

scholarly journals Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

4OR ◽  
2021 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Smooth Vector ◽  
Duality Results ◽  
Vanishing Constraints ◽  
Multiobjective Programming Problems

AbstractIn this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond–Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses.

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